The most likely reason is a combination of two things: that air is trapped
under the raindrop, and that there are some impurities in the water
(certainly the case in a public swimming pool). Contrary to popular belief,
raindrops are not teardrop-shaped. Because they are moving through the air
fairly quickly, and, being water, are easily deformed, they tend to take on
a shape more like a jelly-filled donut or a pizza pop as they fall. The
leading (bottom) edge of the raindrop is fairly flat on its bottom center.
The swimming pool water itself is not smooth, and has little rises and
hollows in it because it is being constantly agitated. So it is not hard for
a small bubble of air to be trapped underneath, which then rises to the
surface. In absolutely pure water this bubble would wink out of existence
very quickly, but if there are impurities in the water, ie, shampoo
residues, the bubble will be able to remain intact for a while. What you may
also be seeing is water droplets floating on the surface of the water. Water
with a thin layer of oil (which swimmers contribute freely to the water) on
top will momentarily prevent the tiny droplets which form when a raindrop
splashes into the water from rejoining the water in the pool, and the
droplets may skitter around on the surface of the water for up to several
seconds.
You can try both of these at home, by using an eyedropper to drip water into
a bowl of water which has a very small drop of detergent or cooking oil
added. Have fun!